Quantum mechanics is thought to be universal. It ought to apply to particles trapped in the Earth’s gravitational field just as it does to electrons trapped in the electric field of an atom. Like atomic electrons, very cold neutrons sitting in a gravitational potential well ought to have quantized energy levels. The experimenter’s problem, of course, is that the gravitational force on a neutron at sea level is 19 orders of magnitude weaker than the Coulomb force on an electron in the ground state of the hydrogen atom. Whereas the low-lying hydrogen energy eigenstates are separated by electron volts, the analogous neutron states in a gravitational well would be separated by only picoelectron volts (1 peV = 10−12 eV).
More than 20 years ago, Vladislav Luschikov and Alexander Frank at the Joint Institute for Nuclear Research in Dubna, near Moscow, suggested that one might exploit the then-new technology of...
